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Mathematics of the USSR-Izvestiya, 1988, Volume 30, Issue 2, Pages 263–281
DOI: https://doi.org/10.1070/IM1988v030n02ABEH001008
(Mi im1294)
 

This article is cited in 23 scientific papers (total in 23 papers)

Spaces of analytic functions of prescribed growth near the boundary

V. V. Napalkov
References:
Abstract: Let $D$ be an arbitrary bounded convex domain in the plane $\mathbf C$. For a certain sequence of convex functions $\varphi=\{\varphi_j\}_{j=1}^\infty$, $\varphi_j(z)\geqslant\varphi_{j+1}(z)$, given on $D$ the space $H_\varphi (D)$ is constructed as the projective limit of the normed spaces
$$ H_j(D)=\{f(z)\in H(D):\|f\|_j=\sup_D|f(z)|\exp{(-\varphi_j(z))}<\infty\},\qquad j=1,2,\dots, $$
where $H(D)$ is the space of analytic functions on $D$. The space $H_\varphi^*(D)$ is described in terms of Laplace transforms. A special role in this description is played by a generalization, proved in the article, of the Paley–Wiener theorem to the case of spaces of infinitely differentiable functions with prescribed growth near the boundary. The result is used in questions involving expansions of functions in Dirichlet series.
Figures: 1.
Bibliography: 17 titles.
Received: 15.01.1985
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1987, Volume 51, Issue 2, Pages 287–305
Bibliographic databases:
UDC: 517.54
MSC: Primary 30B50, 46E10; Secondary 30D15, 49A10, 46A12
Language: English
Original paper language: Russian
Citation: V. V. Napalkov, “Spaces of analytic functions of prescribed growth near the boundary”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 287–305; Math. USSR-Izv., 30:2 (1988), 263–281
Citation in format AMSBIB
\Bibitem{Nap87}
\by V.~V.~Napalkov
\paper Spaces of analytic functions of prescribed growth near the boundary
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 2
\pages 287--305
\mathnet{http://mi.mathnet.ru/im1294}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=896998}
\zmath{https://zbmath.org/?q=an:0638.30050|0623.30054}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 2
\pages 263--281
\crossref{https://doi.org/10.1070/IM1988v030n02ABEH001008}
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  • https://doi.org/10.1070/IM1988v030n02ABEH001008
  • https://www.mathnet.ru/eng/im/v51/i2/p287
  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:538
    Russian version PDF:160
    English version PDF:23
    References:69
    First page:1
     
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